A mathematical model modeling this anatomy was developed in the 1960s in the United States by Aerospace Medical Research Laboratories in Dayton, Ohio. This model, well known as the Hanavan model, describes in a parametric manner, in relation to a given human size and weight, the dimensions of all the parts of the body. In particular, the ankle is described as a joint having three degrees of freedom in rotation. The dimensions of the leg, the part of the body extending between the knee and the ankle, are also described. For example, for a 14-year-old adolescent, 1.6 m tall, and weighing 50 kg, the leg can be represented by a truncated cone with a height of 392 mm, with 29 mm for the small radius and with 47 mm for the large radius. The foot is modeled by a set of rectangular parallelepipeds of which the overall length is 243 mm, the width is 80 mm, the heel height is 62 mm, and the distance between the back of the foot and the connection to the ankle is 72 mm. The height of the leg is defined as the distance between the ankle joint and that of the knee.
At the present time, many humanoid robots have been developed, but none of them complies with the Hanavan model, notably in the space requirement of the leg. For example, robots are found in which the ankle is reduced to an universal joint type, that is to say comprising only two degrees of freedom, a rotation in the sagittal plane and a rotation in the frontal plane. Moreover, the actuation mechanisms used to motorize these two degrees of freedom extend beyond the dimensions specified in the Hanavan model.
The design of the ankle is one of the most difficult problems in the design of a humanoid robot. This is due on the one hand to the fact that the ankle is the joint that needs the most torque in the locomotive apparatus and, on the other hand, because of the constraints of size and weight. For example, a dynamic calculation shows that, to achieve a walk at a speed of 1.2 m/s, for a 1.6 m and 50 kg robot, it is necessary to produce a torque of almost 80 N·m for the rotation in the sagittal plane, with a speed of 4.5 rad/s and an joint range of movement of minus ten degrees to plus thirty degrees.